Half bin linear frequency discriminator

ABSTRACT

Frequency discriminator based on a variant of the DFT transform in which the usual twiddle factors are replaced with twiddle factors as for a DFT on a number of points which is the double as the actual number of sample points. The DFT so modified allows half-bin frequency discrimination, with few added computational burden. Two DFT shifted of half bin with respect to the zero frequency provide a linear response of the discrimination and good immunity to noise. The discriminator is particularly useful in FLL for tracking signals in a GPS receiver.

REFERENCE DATA

This application claims priority from European Patent application No2005EP-101463 of Feb. 25, 2005, the contents whereof are herebyincorporated by reference.

FIELD OF THE INVENTION

The current invention relates to a method of estimating the frequency ofa signal, and to the corresponding device. In particular, but notexclusively, the present invention relates to the application of theaforementioned method and device to the acquisition and tracking oflocalization signal like, for example, the signal emitted from one ormore GPS (Global Positioning System) satellites, or the signal involvedin another radio localization system.

DESCRIPTION OF RELATED ART

The frequency estimate, in particular the frequency estimate ofsinusoidal signals, is an operation used in a large number ofapplications.

Functionally speaking, the term frequency discriminator is employed hereto indicate an algorithm or a mathematical operation that, applied to avector containing a sampled signal, is able to estimate the fundamentalfrequency of the signal itself. Similarly, the term frequencydiscriminator may also indicate, in the contest of this invention, aportion of software for determining the frequency of a signalrepresented for example by a series of time samples. The term frequencydiscriminator also designates in the following, when referred to adevice, an element of electronic circuitry arranged or programmed in amanner as to estimate the fundamental frequency of an analogue ordigital signal present to its input.

An example of utilization of a frequency discriminator is the FLL(Frequency Locked Loop) represented schematically in FIG. 1. In thisexample an incoming signal 42 is combined 45 with the signal of a localoscillator 44 in a mixer 45. The resulting difference frequency isapplied to a frequency discriminator 47. The result of the frequencydiscriminator is in principle proportional to the fundamental frequencyof the input, and is used to drive the local oscillator in a feedbackloop comprising the filter 49 so that it is tuned at the same frequencyas the received signal.

An important application of frequency discriminator is in the Carriertracking loop of GPS receivers. The operation of GPS receivers usuallycomprises an acquisition mode, in which the signal received from theSpace Vehicles (SV) are searched, and a tracking mode, in which theacquired signals are followed both in carrier frequency or phase and incode phase.

The frequency of the signal received from SV in a GPS system is inprinciple affected by a number of instrumental errors, for examplefrequency bias and drift of the local oscillators, as well as by aphysical Doppler shift, related to the relative speed between the SV andthe receiver, which must be appropriately measured, in order to maintaintracking of the SV and arrive at a position determination. This iscommonly realized, in GPS receivers, by means of PLL and FLL feedbackloops.

Typically, the FLL loop is used during the acquisition phase, in reasonof its superior noise immunity. The PLL provides better trackingperformances when the signal strength is adequate. A FLL fallback modeis often provided, as a substitute of the PLL, for tracking weaksignals, and during dynamic peaks due to the motion of the receiver.

In a large number of applications the frequency estimation is done byapplying the frequency mathematical definition of the frequency as thetime-derivative of the phase, f={dot over (φ)}. The incremental ratio ofthe phase is then taken as an estimator of the frequency.$\begin{matrix}{{f( {x,t_{n}} )} = \frac{{\varphi\quad( {x,t_{n}} )} - {\varphi( {x,t_{n - 1}} )}}{\Delta\quad t_{n;{n - 1}}}} & (1)\end{matrix}$

This approach, however, is not practically available when noise exceed acertain threshold, in which case the phase signal is not clearlydetectable

Another possible method implies the extraction of one or more DFT(Discrete Fourier Transform) of the input signal. Frequencydiscriminators based on such methods are however affected bynonlinearities or instabilities, particularly in the neighbourhood ofthe zero frequency, as it will be explained in more detail later.

It is therefore an aim of the present invention to provide a frequencydiscriminator free from the shortcomings of known methods and devices ofthis type.

It is a further object of the present invention to provide a frequencydiscriminator exhibiting a linear response in its operating range.

It is another object of the present invention to provide a frequencydiscriminator having a good immunity to noise.

BRIEF SUMMARY OF THE INVENTION

The above objects are attained by a frequency discriminator methodhaving the feature of the attached independent method claim, and by thecorresponding device and software. Further optional features are theobject of dependent claims.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will be better understood by the examples set out in thedescription and illustrated by the drawings, in which:

FIG. 1 diagrammatically shows a known FLL including a frequencydiscriminator.

FIG. 2 represents the absolute value of the transfer function of threeDFT operations centred on three adjacent frequency bins.

FIG. 3 shows the response of a frequency discriminator based on two ofthe DFT of FIG. 2, in ideal noiseless conditions.

FIG. 4 shows the gain of the discriminator of FIG. 3.

FIG. 5 shows the behaviour of the discriminator of FIG. 3 in presence ofnormal distributed noise.

FIG. 6 shows the response of a frequency discriminator based on thethree DFT of FIG. 2, in ideal noiseless conditions.

FIG. 7 shows the behaviour of the frequency discriminator of FIG. 6, inpresence of normal distributed noise.

FIG. 8 shows the absolute value of the of three DFT operations shiftedof half frequency bin.

FIG. 9 shows the response of a frequency discriminator based on the twoextreme DFT of FIG. 8.

FIG. 10 shows the gain of the discriminator of FIG. 8.

FIG. 11 shows the behaviour of the frequency discriminator of FIG. 8, inpresence of normal distributed noise.

FIG. 12 schematically shows a receiving and tracking module of a GPSreceiver according to an aspect of the present invention.

FIG. 13 schematically represents a frequency discriminator modulecomprised in the receiver of FIG. 12.

DETAILED DESCRIPTION OF THE INVENTION

It is known to use Discrete Fourier Transform (DFT) to realize afrequency discriminator on digital signals. Conceptually, this class ofdiscriminators is based on the principle of comparing the output of atleast two distinct DFT operations, centred at different frequencies.

The DFT is a discrete estimation of a single spectral component of aninput signal, equivalent to one single element of a Fourier transform.

More precisely, if {x_(i)} is a discrete sequence of complex values,corresponding to N samples of a complex signal, the channel-k DFT of{x_(i)} is defined by $\begin{matrix}{{{DFT}( {x,k} )} = {{{\sum\limits_{i = 0}^{N - 1}{x_{i} \cdot ( {{\sin\quad( \frac{2\quad{\pi \cdot k \cdot i}}{N} )} + {{j \cdot \cos}\quad( \frac{2\quad{\pi \cdot k \cdot i}}{N} )}} )}} - N} \leq k < N}} & (2)\end{matrix}$or, in compact formDFT(x,k)=Σ^(N−1) _(i=0) x _(i) W ^(k,i) _(N)  (3)where$\begin{matrix}{W_{N}^{k \cdot {\mathbb{i}}} = {\mathbb{e}}^{{- j}\frac{2\quad{\pi \cdot k \cdot {\mathbb{i}}}}{N}}} & (4)\end{matrix}$

The DFT can therefore be regarded as a linear combination of the samplesx_(i) in which the weights W, also indicated as “Twiddle factors”, arethe N distinct roots of order N of unity in the complex field, taken inincrements of k.

Referring now to FIG. 2, it is possible to appreciate the frequencyresponse of three distinct DFT operators 50 a, 50 b and 50 c, centred onthree consecutive frequency bins corresponding to k=−1, k=0, and k=1,respectively. Analytically, in the case where the samples are equallyspaced, and indicating the sampling period with T, the amplituderesponse curve of each DFT is given by. $\begin{matrix}\begin{matrix}{{R_{k}(f)} = {N \cdot {\frac{{Sin}\quad( {2 \cdot \pi \cdot ( {{f \cdot T} - \frac{k}{N}} )} )}{2 \cdot \pi \cdot ( {{f \cdot T} - \frac{k}{N}} )}}}} \\{= {{{{N \cdot {{\sin\quad c( {{f \cdot T} - \frac{k}{\quad N}} )}}}\quad{with}} - \frac{N}{2}} < k < \frac{N}{2}}}\end{matrix} & (5)\end{matrix}$

The response of each DFT has thus a central peak 502 at f=k/NT, andsecondary maxima 504. The response of the DFT operator is strictly zerofor any frequency multiple of the DFT bin width 1/NT, apart the centralpeak frequency.

The extraction of the absolute value is used to extract the realnon-negative amplitude value of the complex DFT output.

A possible manner of building a DFT frequency estimator involves theevaluation of the quantity $\begin{matrix}{f_{x} = \frac{{{DFT}_{D}(x)} - {{DFT}_{U}(x)}}{{{DFT}_{D}(x)} + {{DFT}_{U}(x)}}} & (6)\end{matrix}$

where DFT_(D) and DFT_(U) stand for the operators |DFT(x,−1)| and|DFT(x,+1)| that is to say, the DFT corresponding to curves 50 a and 50c of FIG. 2.

In the discriminator of equation (6), the frequency is estimated bymeans of the amplitude difference between the two DFT having k=+1 andk=−1. The difference is then normalized using the sum of the two DFTamplitudes.

FIGS. 3 and 4 show the theoretical response of the discriminator ofequation (6), and the relative gain. An advantage of this discriminatoris that the response is strictly linear, i.e the gain is constant, inthe frequency range from f=−1/(NT) to f=1/(NT).

A strong limitation of this approach is however that, in the frequencyregion close to f=0, both DFT are tending to zero, making the differencenoise dominated. This problem is amplified by the fact that thenormalization factor also tends to zero, due to the shape of theresponse R_(x). The result is therefore mathematically undetermined inthe vicinity of f=0. FIG. 5 shows the same response as FIG. 3, but withthe addition of simulated random noise in the input signal. It isapparent that this discriminator provides essentially random result forfrequencies close to f=0.

The discriminator of equation (6) has therefore a point of instabilityin the middle of its frequency range and is therefore useless in mostpractical applications. A way to obviate to this problem is to add theDFT 50 c corresponding to k=0 in the normalization factor thus:$\begin{matrix}{f_{x} = \frac{{{DFT}_{D}(x)} - {{DFT}_{U}(x)}}{{{DFT}_{D}(x)} + {{DFT}_{0}(x)} + {{DFT}_{U}(x)}}} & (7)\end{matrix}$

The response of discriminator of equation (7) is shown in FIG. 6 and,with the addition of simulated noise, in FIG. 7. Noise immunity is nowsatisfactory, however the discriminator has essentially no gain forfrequencies very close to f=0. In some application this fact can bepenalizing, in particular it will induce a hysteresis in the FFL loop ofFIG. 1.

According to the present invention, the frequency discriminatorcomprises the evaluation of two Half-bin Discrete Fourier Transform(HDFT) at different frequencies, wherein the half-bin DFT are defined byformula (3) above, in which the index k takes a half/integer value.

In particular:HDFT(x,−1/2)=Σ^(N−1) _(i=0) x _(i) ·W ^(−i/2) _(N)HDFT(x,1/2)=Σ^(N=−1) _(i=0) x _(i) ·W ^(i/2) _(N)  (8)

However, examination of the expression defining the twiddle factors Wreveals that $\begin{matrix}{W_{N}^{\frac{k}{2} \cdot {\mathbb{i}}} = W_{2 \cdot N}^{k \cdot {\mathbb{i}}}} & (9)\end{matrix}$

The HDFT is thus calculated in the same manner as the ordinary DFT, butthe twiddle factors Ware taken as if the order of the Fourier transformwas 2N, instead of N.

The frequency response of the HDFT (in absolute value) is still given byequation (5).

More precisely we define: $\begin{matrix}{{{H_{U}(x)} = {\sum\limits_{i = 0}^{N - 1}{x_{i} \cdot {\mathbb{e}}^{{- j}\frac{2\quad{\pi \cdot i}}{2N}}}}}{{H_{D}(x)} = {\sum\limits_{i = 0}^{N - 1}{x_{i} \cdot {\mathbb{e}}^{j\frac{2\quad{\pi \cdot i}}{2N}}}}}{or}{{H_{U}(x)} = {\sum\limits_{i = 0}^{N - 1}{x_{i} \cdot W_{2N}^{i}}}}{{H_{D}(x)} = {\sum\limits_{i = 0}^{N - 1}{x_{i} \cdot W_{2N}^{- i}}}}} & (10)\end{matrix}$

The formulation of the frequency discriminator becomes then:$\begin{matrix}{{f(x)} \cong \frac{{{H_{D}(x)}} - {{H_{U}(x)}}}{{{H_{D}(x)}} + {{H_{U}(x)}}}} & (11)\end{matrix}$

However, the peak frequencies are centred on half-integer values of theDFT bin width 1/NT.

The frequency extraction operators H_(D) and H_(U) involve the linearcombination of the samples x_(i) with weights, or twiddle factors, whichare N complex roots of unity from the 2N distinct roots of unity oforder 2N.

FIG. 8 shows for example the response HDFT 55 a corresponding to k=−1/2and 55 c, corresponding to k=1/2. Curve 55 b, corresponding to k=0 isidentical to curve 50 b of FIG. 2.

It will be appreciated that, in contrast with DFT curves of FIG. 1, thecurves 55 a and 55 c do not go to zero simultaneously for f=0. Thisallows the construction of a half-bin frequency discriminator with theresponse and the gain shown in FIGS. 9 and 10.

Advantageously, the half-bin discriminator of the invention exhibits alinear response along all the operating range going from f_(D)=−1/2NT tof_(U)=1/2NT and is stable in the entirety of his operating range, sincethe denominator of equation (11) is not tending to zero for f=0. FIG. 11shows the behaviour of the half-bin discriminator of the invention, inpresence of normal distributed noise

The mathematical formulation of the “Half Bin DFT” can also be deducedfrom a particular characteristic of the FFT algorithm. A complex FFTtakes a vector of N samples of a signal and calculates N spectral linesat j/NT for 0≦i<N. Sometimes, in order to artificially enhance theresolution of the calculated spectra, an FFT of 2N points is calculatedadding N zeros at the end of the input sample vector. This operation,generates N new spectral lines placed at (2i+1)/2NT for 0≦i<N placedexactly in the middle of two N FFT frequency bins. Considering that theFFT algorithm is nothing more than an optimization and a reorganizationof a bank of N DFTs we can deduce the formulation of the half bin DFT byreplacing the spectral lines 1 and 2N−1 (negative frequency) of a 2Npoints FFT with his equivalent DFT. The 2N point DFT for k=1 and k=2N−1becomes: $\begin{matrix}{{{{DFT}( {x,{{k = 1};{{2N} - 1}}} )} = {{\sum\limits_{i = 0}^{{2N} - 1}{{x_{i} \cdot {\mathbb{e}}^{{- j}\frac{2\quad{\pi \cdot k \cdot i}}{2N}}}\frac{N}{2}}} < k < \frac{N}{2}}}{{{DFT}( {x,{{k = 1};{{2N} - 1}}} )} = {\sum\limits_{i = 0}^{{2N} - 1}{x_{i} \cdot W_{2N}^{k \cdot i}}}}} & (12)\end{matrix}$but considering that the last N points of the input vector are zeros:$\begin{matrix}{{{{DFT}( {x,{{k = 1};{{2N} - 1}}} )} = {{{\sum\limits_{i = 0}^{N - 1}{x_{i} \cdot {\mathbb{e}}^{{- j}\frac{2\quad{\pi \cdot k \cdot i}}{2N}}}} - \frac{N}{2}} < k < \frac{N}{2}}}{{{DFT}( {x,{{k = 1};{{2N} - 1}}} )} = {\sum\limits_{i = 0}^{N - 1}{x_{i} \cdot W_{2N}^{k \cdot i}}}}} & (13)\end{matrix}$

This last formulation is exactly the same as the formulation of the halfbin DFT previously deduced.

The frequency discriminator of the invention thus comprises the steps ofcalculating at least two discrete spectral components of an incomingsignal, preferably two spectral components corresponding to twofrequencies f_(D) and f_(U), symmetrically placed above and under thezero frequency.

Each spectral component is extracted by an operator H_(D) or H_(U),which has a maximum of its response for the desired spectral componentf_(D) and f_(U). The response naturally decreases for differentfrequencies, but in a manner that the response does not go to zero forany intermediate frequency between f_(D) and f_(U). In particular theresponse of H_(D) and H_(U) do not go to zero at the intermediate pointf=0.

Thanks to this feature, the discriminator of the invention can extract afrequency error signal, obtained by a step of calculating the differenceof the absolute-value outputs of H_(D) and H_(U), divided by the sum ofthe absolute-value outputs of H_(D) and H_(U).

Since neither the sum nor the difference of the absolute-value outputsof H_(D) and H_(U) is allowed to go to zero in any point of the rangebetween f_(D) and f_(U), the discriminator so obtained is well-behaved,even considering the inevitable influence of noise, ant its value islinear between f_(D) and f_(U).

By using the HDFT operator described above, the frequencies f_(D) andf_(U) of H_(D) and H_(U) are f_(D)=−1/2NT to f_(U)=1/2NT, that is theyare centred on half-integer values with respect to the natural binningof the sequence of the N incoming digital data {x_(i)}, which aresampled at a T sampling rate.

In a preferred embodiment, the operators H_(D) and H_(U) have the formset out in equation (11) above. However, the operators H_(D) and H_(U)may also be obtained, according to the present invention, from differentmathematical operators, for extracting a frequency component of theincoming signal, as the circumstances may require.

The present invention also comprises a receiver for a radio positioningsystem, in particular a GPS receiver, described now with reference toFIG. 12.

The receiver comprises a receiving antenna 20, adapted to the specificradio signal of the sources in the radio localization system. In a GPSsystem the sources are the orbiting GPS Space Vehicles, emitting aradio-localization signal at 1575.42 MHz. The signal received by theantenna is amplified by the low-noise amplifier 30 and down-converted toan intermediate frequency signal (IF signal) in the conversion unit 35,before being fed to the carrier removal stage 49. Other methods ofprocessing the RF signal, including for example Analogue-to-DigitalConversion, are conventionally known and comprised in the presentinvention.

The IF signal is then fed, among others, to a correlation processor,whose function is to de-spread the signals received from each SV, and toalign them temporally with locally generated copies of the pseudorandomranging codes specific for each SV, for example, in case of a GPSreceiver, the correlation processor has the task of demodulating andtracking the coarse acquisition (C/A) GPS ranging signals. To performsuch alignment, the correlators processor comprises an array of trackingmodules 38, each of which is dedicated, for example to the acquisitionand the tracking of a specific SV.

The various functions of the tracking modules 38 are described in thefollowing with reference to the FIG. 12. It is to be understood,however, that this description is given by way of example only, andshould not be interpreted as a limitation of the present invention. Inparticular the various elements and modules described must be understoodin functional terms, and do not necessarily correspond to physicalcircuit elements. In particular several functions may be carried out bysoftware modules, executed by one or more digital processors.

Also, even if the various tracking modules 38 are here described astotally independent and parallel, for the sake of clarity, it must beunderstood, however, that some features or resources can be shared amongtracking modules, as the circumstances require.

Each tracking module has a carrier removal stage 49 comprising,conventionally, a local NCO 40, for generating a local oscillatorsignal, and a 90° phase shifter 41, producing a quadrature replica ofthe local oscillator signal. In a possible variant, the 90° phase shiftmay be done in a external front-end circuit. The incoming radio signalis multiplied with the in-phase and with the quadrature local oscillatorsignal in the multipliers 44, respectively 42, to produce a basebandin-phase signal and a baseband quadrature signal. In tracking mode, thefrequency or phase of the NCO 40 is locked to the carrier frequency orphase of the tracked SV.

Each tracking module 38 comprises also a local Gold pseudorandom codegenerator 50, for generating a local replica of the C/A codecorresponding to a particular GPS Space Vehicle. The Gold pseudorandomcodes can be generated internally, for example by a tapped shiftregister, or, equivalently, extracted from a preloaded table or by anyother technique.

The Gold code generator 50 comprises an independent numericallycontrolled C/A clock whose frequency is set to produce a C/A code at achipping rate of 1.023 MHz. The incoming IF signal is multiplied by thein-phase (I) and quadrature (Q) components of the local carrier and bythe local C/A code. During tracking the local C/A code need to betime-locked to the C/A code received from the SV. The local carrierfrequency and phase need to be locked to the frequency and phase of thecarrier of the received signal, to compensate for Doppler shift on theSV signal and local oscillator frequency drift and bias.

The correlation data for the in-phase signal and for the quadraturesignal can be regarded as the real and imaginary part of a complexsignal. In an ideal frequency lock condition, the frequency of the NCO40 and the frequency of the carrier are identical, and the signalpresent at the input of the discriminator 70 is a pure baseband signal,whose fundamental frequency is zero. During tracking the discriminatormodule 70 produces a frequency error signal 65 which is used for drivingthe NCO 40 of the carrier removal stage in a feedback loop, in order tolock to the frequency of the received signal.

Frequency control device, comprising a variable frequency source (44), amixer (45) for combining an input frequency (42) with an output of thevariable frequency source (44), a discriminator according to one ofclaims 9 to 11 comparing an output signal of the mixer and generating afrequency error signal, for driving the variable frequency source (44)and locking it to the input frequency (42).

According to the invention, the discriminator module 70, now describedwith reference to the FIG. 13, comprises a frequency discriminator basedon the HDFT as described above. More particularly, the discriminatormodule 70 of the invention extract at least two discrete spectralcomponents of the incoming signal, preferably two spectral componentscorresponding to two frequencies f_(D) and f_(U), symmetrically placedabove and under the zero frequency.

Each spectral component is extracted by a frequency extraction means 702or 704, which have a maximum response for the desired spectral componentf_(D), respectively f_(U). The response naturally decreases fordifferent frequencies, but in a manner that the response does not go tozero for any intermediate frequency between f_(D) and f_(U). Inparticular the response of the frequency extraction means 702 and 704 donot go to zero at the intermediate point f=0.

Thanks to this feature, the discriminator of the invention can extract afrequency error signal, obtained by the comparison means 706 which arearranged for calculating the difference of the absolute-value outputs of702 and 704, and preferably for normalizing the difference by dividingit by the sum of the absolute-value outputs of frequency extractionmeans 702 and 704.

Even if, for the sake of simplicity, this example shows the frequencyextraction means 702 and 704 as separate entities, it is to beunderstood that the present invention may also comprise a singlefrequency extraction means, which extracts the two required spectralcomponents f_(D), f_(U) in turn. In practical embodiments, the frequencyextraction means will often consist of a software module, which containscode for calculating the values H_(D) and H_(U), when executed by amicroprocessor.

By using the HDFT operator described above, the frequencies f_(D) andf_(U) are f_(D)=−1/2NT to f_(U)=1/2NT, that is they are centred onhalf-integer values with respect to the natural binning of the sequenceof the N incoming digital data {x_(i)}, which are sampled at a Tsampling rate.

In a preferred embodiment, the frequency extraction means 702 and 704implement the operators H_(D) and H_(U) that have the form set out inequation (11) above. However, the operators H_(D) and H_(U) may also beobtained, according to the present invention, from differentmathematical operators, for extracting a frequency component of theincoming signal, as the circumstances may require.

The frequency discriminator of the invention is based on a variant ofthe DFT transform in which the usual twiddle factors are replaced withtwiddle factors as for a DFT on a number of points which is the doubleas the actual number of sample points. The DFT so modified allowshalf-bin frequency discrimination, with few added computational burden.Two DFT shifted of half bin with respect to the zero frequency provide alinear response of the discrimination and good immunity to noise. Thediscriminator of the invention is particularly useful in FLL fortracking signals in a GPS receiver.

According to the circumstances, the discriminator module 70 may berealized as a dedicated electronic digital circuit, or as amicrocontroller device, programmed in a manner as to carry out the stepsof the method of the invention. The invention also comprises a softwarecode, which can be loaded in the program memory of a computer device,for executing the steps of set forth above when the program is executed.

1. Method of obtaining a frequency difference between an input signaland a reference frequency, comprising the steps of: applying a firstoperator for extracting a discrete spectral component of the inputsignal at a lower frequency and a second operator for extracting adiscrete spectral component of the input signal at a upper frequency,the upper frequency and the lower frequency being placed above and underthe reference frequency, whereas each of the first and second operatorshas a maximum of its response for the corresponding spectral component;calculating the difference of the two spectral component's frequenciesfor obtaining a error value depending on the distance between the inputsignal's fundamental frequency and the reference frequency.
 2. Methodaccording to the preceding claim, further characterized in that: theresponse of first and second operators does not go to zero for anyintermediate frequency comprised between the upper frequency and thelower frequency.
 3. Method according to the preceding claim,characterized in that the upper frequency and the lower frequency aresymmetrically placed around the reference frequency.
 4. Method accordingto claim 1, characterized in that the error value is linearly dependentfrom the distance between the input signal's fundamental frequency andthe reference frequency.
 5. Method according to claim 1, characterizedin that the reference frequency is the zero frequency.
 6. Methodaccording to claim 1, characterized in that the two operators comprise astep of calculating an absolute value of the output.
 7. Method accordingto claim 1, comprising a step of dividing the error value by the sum ofthe two spectral components from the first and second operators. 8.Method according to claim 1, characterized in that the input signalcomprises a number of N successive samples, and in that first and secondoperators comprise a linear combination of the samples, with weightfactors taken from the 2N distinct complex roots of unity of order 2N.9. Method according to the preceding claim, in which the first andsecond operators are given by the formula${H_{U}(x)} = {\sum\limits_{i = 0}^{N - 1}{x_{i} \cdot {\mathbb{e}}^{{- j}\frac{2\quad{\pi \cdot i}}{2N}}}}$${H_{D}(x)} = {\sum\limits_{i = 0}^{N - 1}{x_{i} \cdot {\mathbb{e}}^{j\frac{2\quad{\pi \cdot i}}{2N}}}}$10. Discriminator device, comprising an input, for receiving an inputsignal, and frequency discriminator means, for generating an outputsignal dependent on the difference from the fundamental frequency of theinput signal and a reference frequency; wherein the frequencydiscriminator means comprise frequency extraction means for extracting adiscrete spectral components of the input signal, at a lower frequencyand at a upper frequency, the upper frequency and the lower frequencybeing placed above and under the reference frequency, whereas thefrequency discriminator means has a maximum of its response for thecorresponding spectral component; characterized in that: the response ofthe frequency discriminator means does not go to zero for anyintermediate frequency between f_(D) and f_(U).
 11. Discriminator deviceaccording to the preceding claim, wherein the reference frequency is thezero frequency.
 12. Frequency control device, comprising a variablefrequency source, a mixer for combining an input frequency with anoutput of the variable frequency source, a discriminator according toclaim 10 comparing an output signal of the mixer and generating afrequency error signal, for driving the variable frequency source andlocking it to the input frequency.
 13. GPS receiver, comprising adiscriminator according to claim
 10. 14. GPS receiver, comprising afrequency control device according to claim
 12. 15. Computer program forcarrying out the steps of methods of claim 1.